tan Evaluatee 8 sec dv. tan 8 sec e (Use C as an arbitrary constant.)

Q: tan + x Anctan ly =0

A: The given differential equation is,

Q: 11. sec(x) /sec(x)+ tan(x)dx

A: To find the value of the integral ∫secxsecx+tanxdxUsing Integration by partsAccording to it…

Q: Show that the two formulas are equivalent                                                   ∫sec x…

A:

Q: f sec (5x)tan (5x) dx 3 tan 5x + C A. B. C. 13 cos 5x + C 플 sec 5x + C D. csc 5x + C 5

A:

Q: sec2 a tan ydx+ sec? y tan rdy = 0.

A:

Q: 69. sin t = sec t < 0

A:

Q: IT y = /tan x then equals dx O 1) sec? 2/tan x 2) -sec? x 2tan x O 3) sec? x /tan x 4) - sec? x Vtan…

A: The given function,   y=tan x

Q: sec2 x tan ydx + sec2 y tan xdy = 0.

A: Topic = Differential equation   Formula used ddxtan x = sec2xddytan y = sec2y∫1xdx=lnx+C

Q: sin 2t Cos 2t I) sec t = 1) sin t COs t

A:

Q: sec2(tan-ly?) dy tan ( tan -ly?) +C 1+y4 A True B) False

A: The given integral,        ∫y sec2tan-1y2 dy1+y4

Q: (d) sec(x) – sec(x) sin²(x) = cos (x)

A:

Q: sec e de 1+ tan 0

A: To find∫secθ1+tanθdθ

Q: tan 2x sec 2x dx Evaluate cos 2x O 1 ,tan 2x e + C 2 2 e tan 2x + C O -2 e sec 2x + C 1 ,tan 2x + C…

A: ∫etan2x sec2xcos2x dx=∫etan2x sec2x sec2x dx     ∵secx=1cosx=∫etan2x sec22x dx Now put,…

Q: 4 tan(x) sec2(x) dx = Select one: а. - 1 2 b. 1 С. 1 d. 1

A: Solve integration

Q: Solve r-t cosx+p tan x = 0, %3D

A:

Q: tan(x²y) = (x + y)³ %3D

A:

Q: (arctan o tan)' = 1 – pi k E z°(k +1/2)pi When differentiating on the Real line is this true?

A:

Q: e* tan (e*) dx sec2 (e*) – 7

A:

Q: sinh x + 10 et cosh x + da e2x 2 100 + sinh? (100

A:

Q: (c) / sec/3 (x) tan' a dx ,1/3,

A:

Q: a . Show that y = sin x, y = cos x, and y = a cos x + b sin x (a and b constants) all satisfy the…

A: a. Given

Q: y = c sinx

A: It is known that ddxsinx=cosx and ddxcosx=sinx. We need to eliminate the arbitrary constant: c from…

Q: 3. f10x-sec(5x) tan(5x²)dx ans : sec(5x²) +c (VF). cot 4. dx ,note: Vx = xr ans : 2 In

A: ∫10x·sec(5x2)tan(5x2)dxlet u=sec(5x2)du=sec(5x2)tan(5x2)·10x  dxdx=dusec(5x2)tan(5x2)·10x Replace dx…

Q: lim tan?(3 + Ar) – tan²3 Ax-0 Ar ib. Compute by interpreting it as a derivative.

A:

Q: 9. Solve 4(sec² x)(3 – tan x)/2 dx by substitution. Remember that the first derivative of tan x is…

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Q: e tan (e") dx /sec² (e¤) – 7

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Q: sec(2x)cot(2x) dx sin(x)cos(x)

A:

Q: tan (sinh x) ) ds (b) cosh a sinh x sinh

A:

Q: Vsec z tan ædx = 3 O None O 2(sec æ) – }(sec æ)* +c 15 11 유(sec z) -5(sec z) +c -(sec 2) 3 + c 10…

A:

Q: 5. J 12 csc (-6х) cot (-6x) dx 6. J2x3 cot х4 dx 7. S xª sec (x5 - 9) dx 8. S tan 3 x dx

A: The given integral are 5) 12 csc(-6x) cot(-6x)  6) 2x3 cot(x4)

Q: (b) y=sec x, y = tan x, x = 0, x =1

A: Refer to the figure shown below:   The (grey) area bounded by the given curves is revolved around…

Q: * 16.PUse FTC Part I to find g'(x) if g(x) = sin t dt.

A:

Q: tan?(x) sec(x)dx trig property 2. 2)

A: We have to solve the integral

Q: sin z coS T Q1-Solve by hospital rule lim

A:

Q: d (sec x) dx 18. Prove that = sec x tan x. %D

A:

Q: tan x 2. (D'+) y %3D

A: We are allowed to solve one question at a time, since you didn't ask for any specific question so…

Q: 19-f(t)=t-sin 2t; 20-f(t)=e" cos 2t.

A:

Q: sec (4x+7) dx tan?(4x +7) a) --cot (tx+7)+c b) cot (4K+9) 1e c) - tan (4x+1)+e d) # tan (4x+7) +e 4

A: We will solve the problem.

Q: 8. A dock is 6 feet above water. Suppose you stand on the edge of the dock and pull a rope attached…

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: ) Evaluate antan L tc 2 - arctan -x3 - 2 tc arctan 3- 2) Evaluate dx 5 arctan arctan x*-5 +C 45 -…

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Q: f. – 1 = tan 0 sec 0 over [0, 2n)

A:

Q: sin(v3t) (b) L-- [tan- )) (a) L dt

A: In this question, we use the properties of Laplace and inverse Laplace transform, find the Laplace…

Q: f sec(5x)tan (5x) dx A. B. cos 5x + C 15 sec 5x + C C. tan 5x + C D. 15 csc 5x + C

A: Properties of integration  ∫f(g(x))g'(x)dx=∫f(t) dt where, t=g(x) ∫secx tanxdx=tanx+C

Q: Verify the identity sinh(x + y) = sinh x cosh y + cosh x sinh y

A:

Q: 32. tan?x sec x dx 7/2 35. cot'x dx

A: Topic :- Integration

Q: Calculate tan x ( sec“ x ) dx using u-substitution with: (i) u = tan x (ii) u = sec x

A: I have stated the used formulas in the solution.

Q: csc t sin 3t dt

A: Solve the following

Q: Prove the identity.   sinh(x+y) = sinh x cosh y + cosh x sinh y

A: To show that sinhx+y=sinhx coshy+coshx sinhy

Q: tan y = (1+x)e* sec y. Solve dx 1+x

A: